Lord Rayleigh on the Nodal Lines of a Square Plate. 169 



network is obtained which the required curves cross diagonally. 

 The execution of this plan requires an inversion of the Table 

 connecting z and x y of which the result is as follows : — 



z. 



X. 



Diflf. 



+ 100 



•5000 





•75 



•3680 



•1320 



•50 



•3106 



•0574 



•25 



•2647 



•0459 



•00 



•2242 



0405 



- -25 



•1871 



0371 



•50 



1518 



•0353 



•75 



1179 



0339 



1-00 



•0846 



•0333 



1-25 



•0517 



•0329 



-1-50 



•0190 



0327 



The system of lines represented by the above values of x 

 (completed symmetrically on the further side of the central line) 

 and the corresponding system for y are laid down in the figure. 



5s 2 ^ 





"*v 







S' 







: J =B' 



1 N/ X' 







"•■*"-»^^ 



_ - »'"" 







> s v , 



\ / 



r ^ j^ 



\ 





^•^ 









/X 



s / > 



[/ \S 



\ 











y 





*v/ \^ 



• / "- 





■s,^ 







S' 







/\ \ 



/ 









^t* 







^V , 



A \ 



£ ? 



\ 















V -K - 



7 l 













z 





\ l\ 



/ / 











/ 















s 



/ 

















/ 









1 



i 



*r- \ 





• 







\ 









r ^H 



• 











\ 









/ 

















\ ,'' 















j^ s 





s, \r 

















\\/ j 



'V y\ 

















f\ / 



V x 







"*^*^^_ 



^^,^0^^ 









/ \ y 



~ l/ST" 















/ 



/(\ r 



k < ■ Mt-t 



\ 



s — 







>>i 



-W ^ 



From these the curves of equal displacement are deduced. At 

 the centre of the square we have z a maximum, and equal to 2 

 Phil. Mag. S. 4. Vol. 46. No. 304. Aug. 1873. N 



